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<b>let </b><font color="Maroon" title="c1">N</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">seq</font> being  <a href="toprns_1.html#NM1" title="TOPRNS_1:NM.1">Real_Sequence</a> of <font color="Maroon" title="c1">N</font>  st <font color="Olive" title="b1">seq</font> is <a href="toprns_1.html#V1" title="TOPRNS_1:attr.1">non-zero</a> holds <br/> <a href="toprns_1.html#K3" title="TOPRNS_1:func.3">-</a> <font color="Olive" title="b1">seq</font> is <a href="toprns_1.html#V1" title="TOPRNS_1:attr.1">non-zero</a></span><br/><b>let </b><font color="Maroon" title="c2">seq</font> be   <a href="toprns_1.html#NM1" title="TOPRNS_1:NM.1">Real_Sequence</a> of <font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">seq</font> is <a href="toprns_1.html#V1" title="TOPRNS_1:attr.1">non-zero</a> implies  <a href="toprns_1.html#K3" title="TOPRNS_1:func.3">-</a> <font color="Maroon" title="c2">seq</font> is <a href="toprns_1.html#V1" title="TOPRNS_1:attr.1">non-zero</a> )</span><br/>



<b>assume </b><a NAME="E1:26"/>
<font color="Maroon" title="c2">seq</font> is <a href="toprns_1.html#V1" title="TOPRNS_1:attr.1">non-zero</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="toprns_1.html#K3" title="TOPRNS_1:func.3">-</a> <font color="Maroon" title="c2">seq</font> is <a href="toprns_1.html#V1" title="TOPRNS_1:attr.1">non-zero</a></span><br/>

<a NAME="E2:26"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="toprns_1.html#K2" title="TOPRNS_1:func.2">*</a> <font color="Maroon" title="c2">seq</font> is <a href="toprns_1.html#V1" title="TOPRNS_1:attr.1">non-zero</a>
 
<b>by </b><i><a class="ref" href="toprns_1.html#T22" target="_self" title="TOPRNS_1:th.22">Th22</a></i>;<br/>
<b>hence </b><a NAME="E3:26"/>
 <a href="toprns_1.html#K3" title="TOPRNS_1:func.3">-</a> <font color="Maroon" title="c2">seq</font> is <a href="toprns_1.html#V1" title="TOPRNS_1:attr.1">non-zero</a>
 <b>by </b><i><a class="ref" href="toprns_1.html#T12" target="_self" title="TOPRNS_1:th.12">Th12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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